On the Feynman-Hellmann theorem in quantum field theory and the calculation of matrix elements

Bouchard, C. , Chang, C. C., Kurth, T., Orginos, K. and Walker-Loud, A. (2017) On the Feynman-Hellmann theorem in quantum field theory and the calculation of matrix elements. Physical Review D, 96(1), 014504. (doi: 10.1103/PhysRevD.96.014504)

Abstract

The Feynman-Hellmann theorem can be derived from the long Euclidean-time limit of correlation functions determined with functional derivatives of the partition function. Using this insight, we fully develop an improved method for computing matrix elements of external currents utilizing only two-point correlation functions. Our method applies to matrix elements of any external bilinear current, including nonzero momentum transfer, flavor-changing, and two or more current insertion matrix elements. The ability to identify and control all the systematic uncertainties in the analysis of the correlation functions stems from the unique time dependence of the ground-state matrix elements and the fact that all excited states and contact terms are Euclidean-time dependent. We demonstrate the utility of our method with a calculation of the nucleon axial charge using gradient-flowed domain-wall valence quarks on the Nf = 2 + 1 + 1 MILC highly improved staggered quark ensemble with lattice spacing and pion mass of approximately 0.15 fm and 310 MeV respectively. We show full control over excited-state systematics with the new method and obtain a value of gA = 1.213(26) with a quark-mass-dependent renormalization coefficient.

• Item Type: Articles (Letter)
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Bouchard, Dr Chris
• Authors: Bouchard, C., Chang, C. C., Kurth, T., Orginos, K., and Walker-Loud, A.
• Subjects: Q Science > QC Physics
• College/School: College of Science and Engineering > School of Physics and Astronomy
• Journal Name: Physical Review D
• Publisher: American Physical Society
• ISSN: 1550-7998
• ISSN (Online): 1550-2368
• Published Online: 12 July 2017
• Copyright Holders: Copyright © 2017 American Physical Society
• First Published: First published in Physical Review D 96(1): 014504
• Publisher Policy: Reproduced in accordance with the publisher copyright policy